Tuesday, August 30, 2016

At least a denumerable number of Infinities and rationals are dense but not complete

The work of Cantor http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf shows that there are at least aleph naught number of infinities.

The Power Set of a set cannot be put into one-to-one correspondence with the set and must be a larger infinity.

Between any two rational numbers another one can be found (dense).  The set of all rationals consists of a set of measure zero on the real line (not complete).

Friday, August 12, 2016

Metaphorically Speaking

According to my Webster’s New Collegiate Dictionary, a Merriam-Webster, “metaphor” has two meanings:

1: a figure of speech in which a word or phrase literally denoting one kind of object or idea is used to suggest a likeness or analogy between them (as in the ship plows the sea) ; broadly: figurative language – compare SIMILE 
2: an object, activity, or idea treated as a metaphor

My copy was copyrighted in 1973.  The current definition can be checked at 

I had trouble in school with metaphors.  They don't come labeled with "like" or "as".  Donald J. Trump is smart.  He went to Wharton.  He probably considers metaphors staples.